SHORTCUT CALCULATIONS AND GRAPHICAL COMPRESSOR SELECTION PROCEDURES

Transcription

1 APPENDIX B SHORTCUT CALCULATIONS AND GRAPHICAL COMPRESSOR SELECTION PROCEDURES B.1 SELECTION GUIDE FOR ELLIOTT MULTISTAGE CENTRIFUGAL COMPRESSORS* * Reprinted from a 1994 Elliott Company sales bulletin. The reference information contained herein is provided as an assist to developing your application. However, Elliott reserves the right to modify the design or construction of the equipment described and to furnish it, as altered, without further reference to the illustrations or information contained herein. A Practical Guide to Compressor Technology, Second Edition, By Heinz P. Bloch Copyright 2006 John Wiley & Sons, Inc. 507

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15 SHORTCUT CALCULATIONS AND SELECTION PROCEDURES 521 B.2 QUICK SELECTION METHODS FOR MULTISTAGE COMPRESSORS* Among the many purely graphical methods of rapidly selecting multistage compressors is one developed around 1965 by Don Hallock of the Elliott Company, Jeannette, Pa. To use these charts, the following quantities must be known: 1. W weight flow, in lb/min or scfm (standard ft 3 /min). 2. P 1 inlet pressure, in psia 3. R p pressure ratio (discharge psia/inlet psia) 4. t 1 inlet temp., in F 5. M mole weight 6. K ratio of specific heats Determine the Inlet cfm, Q1. If W is known, use Fig. B.1, proceeding through P 1, t 1, and M to find Q 1. If scfm is known, use Fig. B.2, proceeding through P 1, t 1, and temperature standard to find Q 1. Determine the Head H. On Fig. B.3, enter R p and proceed through K, t 1, and M as shown. If head H exceeds 80,000 to 90,000, more than one compressor body will be required. Determine the Number of Stages Required. On Fig. B.4, enter head H and proceed through M to read the number of stages required. Round this off to the next-higher even number. Determine the Speed and Size of the Machine. On Fig. B.5, enter Q 1 and read the maximum width in inches. Proceed to the stepped lines and read the rpm and flange sizes. Proceed through the number of stages and read the length of the machine in inches. In the example shown, the icfm is 45,000 and the gas is between propane and chlorine in mole weight. The speed is shown to be 4000 rpm and the flanges are 36 and 24 in. A slightly higher flow requires 3500 rpm and 42- and 30-in. flanges. Determine the Horsepower Requirement. On Fig. B.6, enter W, proceed through Q 1 and H, and read HP. If W is not known, work backward from Q 1 on Fig. B.1 to find W before using Fig. B.6. For uncooled, constant weight flow compression, such as alkylation, wet gas, recycle, or air under 50 psia, the foregoing is sufficient to determine price, size, and driver requirement. For cooled or variable weight flow compression, proceed as follows: Cooled Compression. Assume one cooler and two compression sections, each section handling a pressure ratio equal to the square root of the overall pressure ratio. Determine discharge temperature t 2 from Fig. B.7, proceeding through R p, Q 1, K, and t 1. Assuming that this t 2 is satisfactory, proceed through all the figures for each of the separate sections. Speed and width of the compressor will be dictated by the first sections. The total horsepower is the sum of the sections. * Developed and contributed by Don Hallock, Elliott Company, Jeannette, Pa. Adapted by permission of HP and the Elliott Company. Originally published in the October 1965 issue of Hydrocarbon Processing.

16 522 APPENDIX B FIGURE B.1 If the weight flow of gas W is known, use this chart to find the inlet flow Q 1 (icfm). If one cooler does not depress t 2 sufficiently, or if still more horsepower saving is desired, try two coolers or more. R p per section for a two-cooler three-section arrangement is the cube root of the overall R p ; for a three-cooler four-section arrangement, it is the fourth root. Bear in mind that more than one set of cooler openings is seldom available on a single compressor body. When more than one cooler is chosen, therefore, more than one compressor body is likely to be required. Considerable judgment is required in choosing the number of coolers to use. Once the temperature limits are satisfied, the use of additional coolers becomes a matter of economics between compressor and cooler cost, and horsepower evaluation. Variable Weight Flow. For applications having side flows either in or out, it is necessary to consider each constant flow compression section separately. Mixture temperature to the second section after the first inward side flow must be calculated by finding the discharge

17 SHORTCUT CALCULATIONS AND SELECTION PROCEDURES 523 FIGURE B.2 If the scfm value is known, use this chart to find the inlet flow Q 1 (icfm). temperature of the first section from Fig. B.7, multiplying by the first section weight flow, adding in the product of the sidestream temperature and weight flow, and dividing by the sum of the weight flows. With mixture t 1, P 1, W, M, and K known, the figures can now be used for the second section, and so on through the machine. M and K of the sidestream will generally be the same or quite close to those of the inlet, so mixture calculations for these quantities will normally be unnecessary. For extraction side flows, the second section inlet conditions are the same as the first section discharge conditions, except for W. Normally, the first section will see the largest Q 1, in which case the first section Q 1 will dictate the size and speed of the machine. An occasional refrigeration process, however, will show the second section Q 1 to be the largest. In this case, that Q 1 will dictate machine size and speed. To determine the number of stages required, add the stages for each compression section and add in a blank stage for each large side load. It is impossible to give criteria for exactly what constitutes a large side load, but experience has shown that a typical propylene unit

18 524 APPENDIX B FIGURE B.3 Enter this chart at R p, the pressure ratio (discharge/inlet, psia), to find the head H. FIGURE B.4 Enter this chart with the H value on Fig. B.3 to find the number of stages required.

19 SHORTCUT CALCULATIONS AND SELECTION PROCEDURES 525 FIGURE B.5 Enter this chart at the Q 1 value from Fig. B.1 or B.2 and find the speed, width, length, and flange sizes. will require a blank stage for the first sideload only, whereas a typical ethylene machine may require two blank stages. If the total number of stages, including blanks, exceeds nine, a second machine will probably be required. B.3 DELAVAL ENGINEERING GUIDE TO COMPRESSOR SELECTION* * Reprinted by permission of IMO Industries, Inc., DeLaval Turbine Division, Trenton, N.J.

20 526 FIGURE B.6 Enter this chart at the weight flow of gas W and proceed to find the compressor horsepower required.

21 SHORTCUT CALCULATIONS AND SELECTION PROCEDURES 527 FIGURE B.7 The discharge temperature can be found on this chart.

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34 540 APPENDIX B B.4 SHORTCUT (GRAPHICAL) METHOD OF DETERMINING APPROXIMATE PERFORMANCE OF SULZER CENTRIFUGAL COMPRESSORS* The calculation procedures given in the following pages permit To determine: Compressor size and type Nominal diameter D (m) Number of stages z Power input P (kw) Speed n (r/min) Absolute discharge temperature T 2 (K) Using: Mass flow m (kg/s) Suction pressure p 1 (bar abs) Absolute suction temperature T 1 (K) Relative humidity 1 (%) Discharge pressure p 2 (bar abs) Molecular mass M (kg/kmol) Isentropic exponent k Compressibility factor Z The following factors, symbols and indices are also used: Actual suction volume flow V 1 (m 3 /s) Absolute humidity x Peripheral speed u (m/s) Head (polytropic) h p (kj/kg) Temperature difference ( T T c T 1 ) T (K) Intercooling power factor f Indices Suction conditions 1 Discharge conditions 2 Dry t Wet f Polytropic p per casing G per group of stages (between two coolings) S Uncooled * After cooling c Total T Number of casings i Number of intercoolings j How to Use the Diagrams A guide to the selection diagrams and two examples are given in Table B.1, one with air in one casing, the other with gas in two casings. * These graphical methods are intended for screening studies only. Contact the manufacturer for more definitive layout and performance prediction.

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42 TABLE B.1 Selection and Performance Calculation of a Centrifugal Compressor Train Calculation Example 1: Calculation Example 2: Air Compressor, One Casing Gas Compressor, Two Casings Given: Capacity ṁ t 10 kg/s ṁ t kg/s Suction pressure p 1 1 bar abs p bar abs Suction temperature T K T K Relative humidity 1 90% 1 0% Discharge pressure p 2 5 bar abs p bar abs Dry molecular mass M t kg/kmol M t kg/kmol Isentropic exponent c p /c v k 1.4 k 1.29 Compressibility factor Z 1 Z 1 Calculation instructions 1. Determination of the absolute humidity x x x 0 (from T 1, p 1, 1, M t ) with Diagram 1 2. Determination of the wet molecular mass M f 28.7 kg/kmol M t M f kg/kmol M f (from x, M t ) with Diagram 2 3. Calculation of the wet mass flow ṁ f ṁ t (1 x) ṁ f 10( ) f kg/s ṁ f ṁ t kg/s 4. Determination of the max. permissible peripheral speed Electric motor u max 320 m/s Electric motor u max 320 m/s u max (from Z, k, T 1, M f ) with Diagram 3 Turbine u max 290 m/s Turbine u max 290 m/s For further calculation, motor drive has been selected. 5. Determination of the total polytropic head h* pt h* pt 186 kj/kg h* pt kj/kg (from k, p 2, p 1, Z, M f, T 1 ) with Diagram 4 6. Determination of the max. polytropic head obtainable h pg max 300 kj/kg h pg max 300 kj/kg per casing h pg max (from u max ) with Diagram 5 7. Calculation of number of casings i i h pt /h pg max, with h pt i 1 i 2 with f T 0.73 h* pt f T, whereby f T has to be estimated with Diagram 6 8. Determination of the pressure ratio per casing p 2 /p 1G with p 2/p 1T p 2 /p 1G 5 p 2 /p 1G 4.27 Diagram 7 9. Determination of the polytropic head per casing h* pg h* pg h* pt 186 kj/kg h* pg 293 kj/kg (from k, p 2 /p 1G, Z, M f, T 1 ) with Diagram 4 548

43 From now on if two or more casings are necessary, the calculation has to be made for each casing separately (one after the other). First casing Second casing 10. Determination of the influence of intercooling f 0.9 with T 20 f 0.91 with T 0 f 0.91 with T 0 on the required shaft power (from p 2 /p 1G, K, T, T 1 and j 1 and j 1 and j 1 and estimated number of intercoolings per casing j) with Diagram Calculation of the fictive polytropic head h pg h pg H pg h pg h* pg f kj/kg kj/kg Determination of the number of stages z per casing z 4 z 6 z 6 and the definite peripheral speed u (from h pg, z u) u 295 m/s u 304 m/s u 304 m/s with Diagram 8 (round off z to whole number and correct peripheral speed correspondingly) 13. Determination of the actual suction volume V. 1 V m 3 /s V m 3 /s V m 3 /s (from ṁ f, p 1, T 1, M f, Z) with Diagram Selection of the compressor size (nominal diameter D) D 56 cm D 112 cm D 56 cm as a function of V. 1 with Diagram Type designation (from steps 10, 12, 14) RZ 56-4 RZ RZ u Calculation of the speed n (D in meters) 5184 r/min n r/min 0.56 n 1.12 n D r/min 17. Determination of the power input P (from h pg, ṁ f ) P 2173 kw P 8100 kw P 8100 kw with Diagram 11 Total train kw 18. Determination of the discharge temperature T 2 T K T K T K (from p 2 /p 1 between intercooling, k, T 1 ) with with T K with T K with T K Diagram 12 whereby T 1 is the suction temperature and p 2 /p and p 2 /p and p 2 /p after preceding intercooling and pressure ratio p 2 /p 1 between intercooling has to be determined with Diagram 7 549